1. Field of the Invention
The invention relates to a variable gain amplifier, and more particularly, to a variable gain amplifier having a linear decibel-scale gain with respect to the controlling voltage(s).
2. Description of the Prior Art
Wireless communication system development continues to rapidly progress. As a result, many types of high band-width high sensitivity transceivers have been proposed. Variable gain amplifiers are often used in these types of transceiver to broaden the processing range of the system. A variable gain amplifier having a linear gain in the decibel (dB) scale with respect to the controlling voltage(s) has the broadest gain range.
Please refer to FIG. 1, where a circuit diagram of a conventional variable gain amplifier is illustrated. The variable gain amplifier shown in FIG. 1 is a differential amplifier. The voltage gain Av of the variable gain amplifier can be determined from the half circuit of the differential amplifier. Disregarding the phase, the voltage gain Av of this variable gain amplifier is:
                    Av        =                              Vout            Vin                    =                      K                          1              +                              exp                ⁡                                  (                                      Vy                    Vt                                    )                                                                                        (        1        )            where K is substantially a constant.
From equation 1 it can be seen that the denominator of the voltage gain Av is not a simple exponential function that it has a constant term “1” in addition to the simple exponential function exp(Vy/Vt). Consequently, the voltage gain Av does not have a simple exponential relationship with the controlling voltage Vy.
Please refer to FIG. 2. FIG. 2 is a graph showing the relationship between the voltage gain Av and the controlling voltage Vy of FIG. 1. Note that when Vy<Vt, the voltage gain Av does not change exponentially with respect to the change in the controlling voltage Vy. The smaller the controlling voltage Vy, the less the voltage gain Av changes with respect to the change in the controlling voltage Vy. The area where the voltage gain Av does not have a perfect exponential relationship with the controlling voltage Vy is caused by the constant term 1 in the denominator of equation 1.
Furthermore, equation 1 contains a term called the thermal voltage Vt, which is a variable that changes in response to the change of temperature. The result is that the relationship between the voltage gain Av and the controlling voltage Vy does not remain constant when temperature changes.